If the targeted permanent or player is an illegal target by the time Banshee's ability resolves, the ability doesn't resolve. You won't be dealt damage.

Banshee : règles, fonctionnement et interactions (MTG)

Banshee is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

, : This creature deals half X damage, rounded down, to any target, and half X damage, rounded up, to you.

How it works : Banshee

Original English text — Wizards of the Coast / Scryfall

#1October 1, 2009· Wizards of the Coast
If the targeted permanent or player is an illegal target by the time Banshee's ability resolves, the ability doesn't resolve. You won't be dealt damage.
No other card is named in this ruling.